Simplify the following expression: $ p = \dfrac{3}{7} + \dfrac{1}{k - 8} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 8}{k - 8}$ $ \dfrac{3}{7} \times \dfrac{k - 8}{k - 8} = \dfrac{3k - 24}{7k - 56} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{1}{k - 8} \times \dfrac{7}{7} = \dfrac{7}{7k - 56} $ Therefore $ p = \dfrac{3k - 24}{7k - 56} + \dfrac{7}{7k - 56} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{3k - 24 + 7}{7k - 56} $ $p = \dfrac{3k - 17}{7k - 56}$